Multivariate data analysis: The French way

TL;DR

This paper introduces the duality diagrams framework for multivariate data analysis, unifying various techniques like discriminant analysis and correspondence analysis, and extends it to regression of graphs on covariates, highlighting French statistical approaches.

Contribution

It presents a unified framework of duality diagrams for multivariate analysis and generalizes it to regression of graphs on covariates, emphasizing French statistical methods.

Findings

Unifies multiple multivariate techniques under duality diagrams.

Generalizes the framework to include regression of graphs.

Highlights differences between French and North American statistical approaches.

Abstract

This paper presents exploratory techniques for multivariate data, many of them well known to French statisticians and ecologists, but few well understood in North American culture. We present the general framework of duality diagrams which encompasses discriminant analysis, correspondence analysis and principal components, and we show how this framework can be generalized to the regression of graphs on covariates.